The Blues were in the market for cover at wing-back this summer, and had been frustrated in previous efforts to sign Alex Oxlade-Chamberlain from the Gunners as one of the candidates for the role.
In a surprise move, Sagna was also seen as an option for Antonio Conte late on in the transfer window, though the move was abandoned when a deal for Zappacosta became possible, according to L’Equipe.
The 34-year-old was released by City at the end of his contract last season, having failed to establish himself as a regular under Pep Guardiola in his final year with the club.
Sagna was previously regarded as one of the finest full-backs in Europe during his time with Arsenal, but no longer looks capable of playing consistently at that level.
The Frenchman is now reportedly being looked at by Leicester City and West Ham after snubbing an offer from Premier League new-boys Brighton.
Chelsea 2017/18 Fixtures
Leicester City (A) – Sat 9 Sep
FK Qarabag – Champions League (H) – Tue 12 Sep
Arsenal (H) – Sun 17 Sep
Nottingham Forest – League Cup (H) – Tue 19 Sep
Stoke City (A) – Sat 23 Sep
Atletico Madrid – Champions League (A) – Wed 27 Sep
Man City (H) – Sat 30 Sep
Crystal Palace (A) – Sat 14 Oct
Roma – Champions League (H) – Wed 18 Oct
Watford (H) – Mon 23 Oct
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Although the transfer window closed last week, unattached players are still allowed to move and discuss deals in between the summer and January, so Sagna could find himself a new club soon.
Having been in England since joining Arsenal from Auxerre all the way back in 2007, it seems Sagna is keen to continue playing in the Premier League.
While a surprise move to Chelsea ultimately fell through, he now looks set to chosse between Leicester and West Ham in due course.